Column Vector

Definition: Column Vector

An $m\times 1$-matrix of the form

$$\left[\begin{array}{c}{v}_1\\ ⋮\\ v_m\end{array}\right]\in F^{m\times 1}$$

is called a column vector.

NOTATION

Column vectors are usually denoted as $\vec{u},\vec{v}$, etc.

In the context of column vectors, $F^{m\times 1}$ is usually denoted as just $F^m$.

Definition: Component

The number $v_k$ ($k=1,\dots ,m$) is known as the $k$-th component of the vector.